JEE PYQ: Electrostatics Question 31
Question 31 - 2020 (08 Jan Shift 1)
In finding the electric field using Gauss law the formula $|\vec{E}| = \frac{q_{\text{enc}}}{\varepsilon_0|A|}$ is applicable. In the formula $\varepsilon_0$ is permittivity of free space, $A$ is the area of Gaussian surface and $q_{\text{enc}}$ is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?
(1) Only when the Gaussian surface is an equipotential surface.
(2) Only when the Gaussian surface is an equipotential surface and $|\vec{E}|$ is constant on the surface.
(3) Only when $|\vec{E}|$ = constant on the surface.
(4) For any choice of Gaussian surface.
Show Answer
Answer: (1)
Solution
The formula $E = \frac{q_{\text{enc}}}{\varepsilon_0 A}$ requires that $\vec{E}$ is constant in magnitude and perpendicular to the surface everywhere, which happens when the Gaussian surface is an equipotential surface. Answer is (1).
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